Problem: $P(t)$ models the distance of a swinging pendulum (in $\text{cm}$ ) from the place it was released $t$ seconds after it starts to swing. Here, $t$ is entered in radians. $P(t) = -5\cos\left(2\pi t\right) + 5$ What is the first time the pendulum reaches $3.5\text{ cm}$ from the place it was released? Round your final answer to the nearest hundredth of a second.
Answer: Converting the problem into mathematical terms $P(t) = -5\cos\left({2\pi}t\right) + 5$ has a period of $\dfrac{2\pi}{{2\pi}}=1$ second. We want to find the first solution to the equation $P(t)=3.5$ within the period $0<t<1$. The answer The equation's two solutions within the desired period (rounded to the nearest hundredth of a second) are $0.20$ and $0.80$. Therefore, the first time the pendulum reaches $3.5\text{ cm}$ is after $0.20$ seconds.